<h2>Problem 141</h2>
<div style="color:#666;font-size:80%;">17 February 2007</div><br />
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<p>A positive integer, <i>n</i>, is divided by <i>d</i> and the quotient and remainder are <i>q</i> and <i>r</i> respectively. In addition <i>d</i>, <i>q</i>, and <i>r</i> are consecutive positive integer terms in a geometric sequence, but not necessarily in that order.</p>
<p>For example, 58 divided by 6 has quotient 9 and remainder 4. It can also be seen that 4, 6, 9 are consecutive terms in a geometric sequence (common ratio 3/2).<br />
We will call such numbers, <i>n</i>, progressive.</p>
<p>Some progressive numbers, such as 9 and 10404 = 102<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" />, happen to also be perfect squares.<br /> The sum of all progressive perfect squares below one hundred thousand is 124657.</p>
<p>Find the sum of all progressive perfect squares below one trillion (10<img src="" style="display:none;" alt="^(" /><sup>12</sup><img src="" style="display:none;" alt=")" />).</p>

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